# Mathematics

## Recommended readings

* Introduction to Linear Algrebra
* [3Blue1Brown](https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw)

## Syntax Guides

* &#x20;<https://github.com/cben/mathdown/wiki/math-in-markdown>
* <https://faculty.math.illinois.edu/~hildebr/tex/course/intro2.html>

$$
a^2 + b^2 = c^2
$$

$$
\alpha + \beta +\delta+\theta +\phi \rho
$$

$$$
Consider (eq:a):

$$ \alpha = \beta $$        (a)
$$$

```
Consider (eq:a):

$$ \alpha = \beta $$        (a)
```

$$
@equation(id)
x = \sum\_{i=1}{N} i
@/
$$

```
@equation(id)
x = \sum_{i=1}{N} i
@/
```

$$
$ y=\sum\_{i=1}^n g(x\_i) $
$$

```
 $ y=\sum_{i=1}^n g(x_i) $
```

$$
\begin{align}
(a+b)^3 &= (a+b)^2(a+b)\\
&=(a^2+2ab+b^2)(a+b)\\
&=(a^3+2a^2b+ab^2) + (a^2b+2ab^2+b^3)\\
&=a^3+3a^2b+3ab^2+b^3
\end{align}
$$

```
\begin{align} 
(a+b)^3 &= (a+b)^2(a+b)\\
&=(a^2+2ab+b^2)(a+b)\\
&=(a^3+2a^2b+ab^2) + (a^2b+2ab^2+b^3)\\
&=a^3+3a^2b+3ab^2+b^3
\end{align}

```

$$
\[
\left|\sum\_{i=1}^n a\_ib\_i\right|
\le
\left(\sum\_{i=1}^n a\_i^2\right)^{1/2}
\left(\sum\_{i=1}^n b\_i^2\right)^{1/2}
]
$$

```
\[
\left|\sum_{i=1}^n a_ib_i\right|
\le
\left(\sum_{i=1}^n a_i^2\right)^{1/2}
\left(\sum_{i=1}^n b_i^2\right)^{1/2}
\]
```